Solve (sqrt{frac{81/25})^2*sqrt[3]{(81/27)^3}}{sqrt{144/36}}=

$$\frac { ( \sqrt { \frac { 81 } { 25 } } ) ^ { 2 } \cdot \sqrt[ 3 ] { ( \frac { 81 } { 27 } ) ^ { 3 } } } { \sqrt { \frac { 144 } { 36 } } } =$$

Evaluate

$$\frac{243}{50}=4.86$$

Solution Steps

The square of \sqrt{\frac{81}{25}} is \frac{81}{25}.

$$\frac{\frac{81}{25}\sqrt[3]{\left(\frac{81}{27}\right)^{3}}}{\sqrt{\frac{144}{36}}}$$

Divide 81 by 27 to get 3.

$$\frac{\frac{81}{25}\sqrt[3]{3^{3}}}{\sqrt{\frac{144}{36}}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{\frac{81}{25}\sqrt[3]{27}}{\sqrt{\frac{144}{36}}}$$

Calculate \sqrt[3]{27} and get 3.

$$\frac{\frac{81}{25}\times 3}{\sqrt{\frac{144}{36}}}$$

Multiply \frac{81}{25} and 3 to get \frac{243}{25}.

$$\frac{\frac{243}{25}}{\sqrt{\frac{144}{36}}}$$

Divide 144 by 36 to get 4.

$$\frac{\frac{243}{25}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\frac{243}{25}}{2}$$

Express \frac{\frac{243}{25}}{2} as a single fraction.

$$\frac{243}{25\times 2}$$

Multiply 25 and 2 to get 50.

$$\frac{243}{50}$$

Factor

$$\frac{3 ^ {5}}{2 \cdot 5 ^ {2}} = 4\frac{43}{50} = 4.86$$